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Simplifying b2 + 12b = 144 Reorder the terms: 12b + b2 = 144 Solving 12b + b2 = 144 Solving for variable 'b'. Reorder the terms: -144 + 12b + b2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 12b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 12b + 144 + b2 = 0 + 144 Reorder the terms: -144 + 144 + 12b + b2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 12b + b2 = 0 + 144 12b + b2 = 0 + 144 Combine like terms: 0 + 144 = 144 12b + b2 = 144 The b term is 12b. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12b + 36 + b2 = 144 + 36 Reorder the terms: 36 + 12b + b2 = 144 + 36 Combine like terms: 144 + 36 = 180 36 + 12b + b2 = 180 Factor a perfect square on the left side: (b + 6)(b + 6) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (b + 6) equal to 13.416407865 and -13.416407865.Subproblem 1
b + 6 = 13.416407865 Simplifying b + 6 = 13.416407865 Reorder the terms: 6 + b = 13.416407865 Solving 6 + b = 13.416407865 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + b = 13.416407865 + -6 Combine like terms: 6 + -6 = 0 0 + b = 13.416407865 + -6 b = 13.416407865 + -6 Combine like terms: 13.416407865 + -6 = 7.416407865 b = 7.416407865 Simplifying b = 7.416407865Subproblem 2
b + 6 = -13.416407865 Simplifying b + 6 = -13.416407865 Reorder the terms: 6 + b = -13.416407865 Solving 6 + b = -13.416407865 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + b = -13.416407865 + -6 Combine like terms: 6 + -6 = 0 0 + b = -13.416407865 + -6 b = -13.416407865 + -6 Combine like terms: -13.416407865 + -6 = -19.416407865 b = -19.416407865 Simplifying b = -19.416407865Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.416407865, -19.416407865}
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